5065 TableI. (H,,H2)Exchange Rate Constantsat l W ° K (cm3/molesec) 0 0 1 0 1 0
3.438 X 1.009 X 1.634 X 1.521 X 1.535 X 1.530 X
0 1 1 2 2 3
lo4 lo6 lo7 lo7 lo8 108
3.268 X 2.397 x 9.695 X 1.117 X 2.816 X 4.285 X
lo4
+
104
lo3 lo4 103 loa
obtained (e.g., K(T) is 1.332 X lo5 cm3/mole sec at 1600°K and 1,164 cm3/mole sec at 1000°K). The values of K(T)are well fitted by an Arrhenius plot with an activation energy (E,) of 61.64 kcal/mole and a preexponential factor ( A ) of 3.475 X lOI3 cm3/mole sec. Thus, E, is only slightly less than the classical barrier height. The absolute rate theory values of the rate constants for the same surface are somewhat smaller than those from the trajectory treatment (e.g., K(r> is 0.643 X lo5 cm3/mole sec at 1600°K and 0.296 cm3/ mole sec at 1000’K). Comparison of our results with the conclusions of Bauer, et al.,2,3shows agreement in that the rate of H2,Hz exchange is greatly enhanced for molecules in excited vibrational states (v and/or v’ > 0) as compared with molecules in the ground vibrational state (v = v’ = 0), the translational and rotational degrees of freedom having thermal distributions; e.g., k,, (v = 0, v’ = 1) is -30 times k,, ( u = 0, v ’ = 0) at T,, = Trot = 1600°K. However, because of the low population of the excited states, the contribution to K(T) from the (v = 0, v ’ = 1) collisions is only 0.74 that from the (v = D’ = 0) collisions at 1600°K and becomes even less at lower temperatures. By summing over the kB values at 1600”K, one finds that kB ( u = v ’ = 0) contributes -25 and all of the excited states 75 of
z
z
KV).
Thus, in contrast to the suggestion of Bauer, et aI.,?t3 there is no theoretical evidence for a “vibrational threshold.” Model calculations show that an increase in the vibrational energy availability is by itself not sufficient to produce such a threshold; lo the translational energy must be significantly less effective as well. Since corresponding results are obtained in calculations on the Hz,Dz system, further studies are clearly needed to resolve the differences between ref 2 and 3 and the present treatment. The calculations reported here are only illustrative because they are based on classical mechanics and employ an approximate potential surface. Thus, it is possible that the results do not provide an accurate description of the Hz,Hz reaction. However, although the absolute value of the rate constant is very sensitive to the potential, particularly to the barrier height, the relative k,, and kB values are much less so. Moreover, it is likely that the calculated efficiency of translational and vibrational energy in overcoming the activation barrier is not atypical for systems in which the reactants and products are similar. For significantly different values, a drastic modification of the potential (10) A vibrational threshold value co would be defined to exist at a temperature T if
2
v’=O
kB(ao
- ti’,
ti’,
uo
T ) >>
-1 kB(U”
U”
3v’=O
- U’, U t , r )
surface would be required.” In more asymmetric reactions (e.g., some endothermic reactions), vibrational energy may have increased importance. An example might be “late-uphill” surface corresponding to CH3 KI 4 K CH31, the inverse of the reaction for which molecular beam studies12 indicate that much of the exothermicity appears as internal excitation of products. However, even in this case the available data when combined with microscopic reversibility arguments are not sufficient to show that the excited vibrational states would dominate the reaction for an equilibrium population in the thermal region. For the nonequilibrium case with an excess of excited molecules, there are likely to be measurable effects for reactions involving a significant activation energy and/or endothermicity. It would be of great interest to have more data on exchange reactions with a non-Boltzmann vibrational population produced by the stimulated Raman effect, “chemical activation,”’4 or electron impact. l 5 A more detailed analysis of the Hz,Hz and Hz,D2 exchange reactions and related high-energy processes (Le., dissociation, exchange dissociation, atomization) will be presented. Acknowledgment. We wish to thank Dr. S . Bauer, Dr. S . Byron, Dr. G. B. Kistiakowsky, Dr. J. Kiefer, and Dr. R. D. Kern for helpful discussion. We gratefully acknowledge the machine time used for these calculations at the Columbia Computing Center.16
0
+
(1 1) Distortions in the surface such that the reaction trajectory is perpendicular to the initial direction of translational motion while climbing the potential barrier could increase the vibrational-translational efficiency ratio. The distortions discussed in ref 7 are unlikely to be of this type; however, if the barrier were as high as in ref 7, an atomic mechanism would be expected. (12) D. R. Herschbach, Adcan. Chem. Phys., 10, 319 (1966). (13) F. De Martini and J. Ducuine. Phvs. Rev. Lefters. 17. 117 11966). Fiowers, Quart. keu. (Londonj, (14) B. S. Rabinovitch and M. 18., 122 ~. - -
11964). - ,
\
(15) H. von Koch and L. Friedmann,J. Chem. Phys., 38, 11IS (1963);
T. Moran and L. Friedmann, ibid., 39,2491 (1963). Although a vibraHz+ -c tional threshold is suggested for the cndsthermic reaction He iHeH+ H, it is not clear that the data require more than a significant change in the reaction cross section Rith Hz+ vibrational state. See also J. C. Light and J. Lin, J . Chem. Phys., 43, 3209 (196S), and J. H. Futrell and F. P. Abramson in “Ion-Molecule Reactions in the Gas Phase,” Advances in Chemistry Series No. 58, American Chemical Society, Washington, D. C., 1966, Chapter 8. (16) Most of the computations were performed while the authors were at Columbia University. (17) National Science Foundation (1965-1966) and National Institutes of Health (19661967) Postdoctoral Fellow.
+
K. Morokuma, L. Pedersen,’? M. Karplus Department of Chemistry, Haruard Unicersity Cambridge, Massachusetts Receiced April 19, 1967
Cobalt(II1) Complexes of Linear Tetramines. 11. Isomerism in the trans-Dichloro(l,4,8,11-tetraazaundecane)cobalt(III) Ion Sir : Quite recently, Sargeson and co-workers have demonstrated the configurational stability of coordinated asymmetric secondary nitrogen by isolating isomers of cobalt(II1) complexes which differ in the configuration about such nitrogen atoms within the complexes.’ In light of their work, our investigations of cobalt(II1) complexes of 1,4,8,1l-tetraazaundecane (2,3,2-tet), (1) D. A. Buckingham, P. A. Marzilli, and A. M. Sargeson, Inorg. Chem., 6 , 1032 (1967), and references therein.
Communications to the Editor
5066
structure I, have provided results which are very informative with respect to the stereochemistry of coordination compounds. Herein, we wish to report these results.
change should occur under the conditions of the aquation reaction, the anation reaction, or the separation procedure. Thus, the only conclusions compatible with these considerations and the above results is that ion is the pure RS(meso) the trans-[Co(2,3,2-tet)Cl~]+ CH2CH2CHZ / \ isomer and the trans-[Co(2,3,2-tet)(H20)C1]2+complexes HN NH are the geometrical isomers predicted for the RS(meso) c~nfiguration.~If the trans-[Co(2,3,2-tet)C12]+had consisted of the RR,SS racemate in addition to the RS(meso) isomer, the trans-(RR,SS)-chloroaquo complexes would have had to be present in one of the two chloroaquo fractions obtained since the other two fractions were found to contain only dichloro and diaquo trans-[Co(2,3,2-tet)Clz]+, prepared by the standard complexes. The trans-[Co( 2,3,2 -tet) Clz]+ complexes air-oxidation technique, 2, undergoes mercury(I1)prepared by anation would then have been different induced aquation in acidic solution to yield a mixture for the two fractions, which is inconsistent with the of products which can be separated into four fractions above results. on a column of Dowex 50W-X2 cation-exchange resin. Cobalt(II1) complexes of 2,3,2-tet having the cis Two of these fractions have been identified in solution structure can be prepared using bidentate ligands to Referring to Figure as trans-[C0(2,3,2-tet)(H~O)Cl]~+. occupy cis octahedral sites in the complexes. Such a 1, which shows the most stable configurations for 2,3,2complex, cis-[Co(2,3,2-tet)COa]Cf, can be prepared by reaction of trans-(RS)-[Co(2,3,2-tet)Cl2lCl with Na2C03 in aqueous solution. Molecular models suggest that for cis structures the R R and SSconfigurations are preferred in the p case and necessary in the a case. Since the basic conditions under which the carbonato complex is prepared should permit rearrangement about the asym\H Y metric nitrogen atoms, the R R and SS configurations are expected for the cis-carbonato complex. The carbonato complex undergoes acid hydrolysis in concentrated hydrochloric acid, under which conditions the configurations about the secondary nitrogen atoms should be retained, to yield cis-[Co(2,3,2-tet)C12]+ which isomerizes, producing a mixture of the cis isomers as well as the trans isomer. Because of the low solubility of the perchlorate salt of the transFigure 1. Configurations of 1,4,8,1l-tetraazaundecane in trans dichloro complex, it can be readily isolated from the octahedral structures. mixture. Although the complex so obtained and trans(RS)-[Co(2,3,2-tet)CI2]C1O4 exhibit indistinguishable visible spectra,6 their infrared spectra' are markedly diftet in trans structures using a projection t e c h n i q ~ e , ~ ferent, which confirms the notion that the former is the it is evident that there are four possible isomers of RR,SS racemate. trans-[Co(2,3,2-tet) (HzO)Cl] 2+ : the two geometrical Thus we have been able to prepare trans-(RR,SS)RS(meso) isomers, resulting from the nonequivalence [C0(2,3,2-tet)Cl~]ClO~~ and trans-(RS)-[Co(2,3,2-tet)Cl~Jof the two trans sites in the R S case, and the R R and C104 by kinetic and thermodynamic routes, respecSS antipodes. The configurations about the asymmettively. These diastereomers exhibit strikingly different ric nitrogen atoms in the trans-chloroaquo products chemical behavior. First, trans-(R R ,SS)-[Co( 2,3,2can be related to the configurations in the transtet)Clz]+ isomerizes to a mixture of cis- and transdichloro complex, from which the chloroaquo products dichloro complexes in concentrated hydrochloric acid were obtained, in the following way. Both products undergoes no strucwhile trans-(RS)-[Co(2,3,2-tet)Clz]+ undergo chloride anation quantitatively in a mixture tural change under the same conditions. Second, the of hydrochloric and perchloric acids to yield sparingly trans-(RK,SS) racemate aquates in acidic solution consoluble trans-[Co(2,3,2-tet)C12]ClO4 salts which exhibit siderably faster than the trans-(RS) isomer; and, moreinfrared spectra indistinguishable from each other as over, aquation in the former case proceeds with quantiprepared by the airwell as truns-[Co(2,3,2-tet)Cl~]ClO~ tative production of cis-chloroaquo complexes inioxidation technique, Since the configurational intialiy, while in the latter case the trans structure is retegrity of coordinated asymmetric secondary nitrogen tained. These observations not only substantiate that atoms is maintained in acid solution, no configurational (2) B. Bosnich, R. D. Gillard, E. D. McKenzie, and G. A. Webb, J . Chem. SOC.,Sect. A , 1331 (1966). ( 3 ) H. G. Hamilton, Jr., and M. D. Alexander, I m r g . Chem., 5, 2060 (1966). (4) The projections are in a plane perpendicular to the CZaxis in the RR and SS cases and perpendicular to the 6, plane in the RS(meso) case. Secondary nitrogen atoms, represented by dots, eclipse the primary nitrogen atoms, represented by circles. For an explanation of the R , S symbolism, see R. S. Cahn, C. I
